CA Foundation · Quantitative Aptitude · Theoretical Distributions
If X follows a normal distribution with mean 40 and standard deviation 8, which value of X corresponds to the standard normal variate Z = -1.5?
The value is 28. Since Z = (X - mean)/SD, X equals the mean plus Z times SD, which is 40 + (-1.5)(8) = 28. A negative Z means the value lies below the mean, so it must be less than 40.
- A28Correct
- B52
- C32
- D48
Explanation
Z = (X - mean)/SD, so X = 40 + (-1.5)(8) = 40 - 12 = 28. Option 52 comes from using +1.5 instead of -1.5. Option 32 comes from subtracting only one SD (40 - 8).
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